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# In a class with 12 boys and 8 girls, a committee will be

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Manager
Joined: 14 Mar 2007
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In a class with 12 boys and 8 girls, a committee will be [#permalink]  27 Jun 2007, 06:46
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In a class with 12 boys and 8 girls, a committee will be chosen with 3 class representatives. The probability of the committee being made up only of girls is:
CIO
Joined: 09 Mar 2003
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Re: PS - proba -solve and explain this is good [#permalink]  27 Jun 2007, 06:53
andrehaui wrote:
In a class with 12 boys and 8 girls, a committee will be chosen with 3 class representatives. The probability of the committee being made up only of girls is:

Probability is number you want/total possible.

Start with total possible: there are 20 people, want committees of 3, that's 20c3, or (20x19x18)/(3x2x1)

Number you want is girls only: 8 people to choose from now, 3 spots, so that's 8c3, or (8x7x6)/(3x2x1)

Put one over the other, cancel out, and you get

56/(20x19x3) whatever that turns out to be.
Manager
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(A) less than 1%
(B) less than 5%
(C) greater than 40%
(D) exactly 40%
(E) approximately 13%

Manager
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Could you explain why do we need to use combinatorics in this case?

The way I'd do it is:
Probability first member is a girl: 8/20
Probability second member is a girl: 7/19
Probability third member is a girl: 6/18

Why is this approach incorrect?

Thanks
CIO
Joined: 09 Mar 2003
Posts: 463
Followers: 2

Kudos [?]: 35 [0], given: 0

Could you explain why do we need to use combinatorics in this case?

The way I'd do it is:
Probability first member is a girl: 8/20
Probability second member is a girl: 7/19
Probability third member is a girl: 6/18

Why is this approach incorrect?

Thanks

because the order doesn't matter for the committee. There are no positions, so the three women come in any order. The way you did it above, you are finding the probability of all female the orderings possible out of all the total orderings possible.
Senior Manager
Joined: 21 Jun 2006
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8C3/20C3

probably the easiest probability question.
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